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3 Answers
3

得る is usually read as える. This is the "modern" verb-form of 得（う） (shimo-nidan).

Conjugation (MZK/RYK/SSK/RTK/IZK/MRK)

Modern: え/え/える/える/えれ/えよ
Classic: え/え/う/うる/うれ/えよ

One thing to note is that for MZK and RTK, either conjugation is え, so you will never-ever read 得ない as "unai" etc, and because you never really see classical SSK in regular text (since SSK and RTK are read the same in modern Japanese) you'll probably never have to read it as 得(う). The only time you read it as うる is if it's a sentence ending or directly modifying something. But again, the うる reading itself is pretty rare. The only thing I tend to see is an occasional あり得る(ありうる), but you can read that as (ありえる) anyway.

For that particular sentence: 彼はとてもよく訓練された役者だけが本当に成功し得ると思っている

^I would guess 'しえる', just because える is more common. し得る on my IME comes up as a candidate for both しえる and しうる.

You can say that something has a possibility of existing by combining
「ある」 and the verb 「得る」 to produce 「あり得る」. This essentially means
「あることができる」 except that nobody actually says that, they just use
「あり得る」. This verb is very curious in that it can be read as either
「ありうる」 or 「ありえる」, however; all the other conjugations such as
「ありえない」、「ありえた」、and 「ありえなかった」 only have one possible reading using 「え」.